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Published at Jul 13 2018
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Instructions

Test suite

Solution

Use the Sieve of Eratosthenes to find all the primes from 2 up to a given number.

The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e. not prime) the multiples of each prime, starting with the multiples of 2.

Create your range, starting at two and continuing up to and including the given limit. (i.e. [2, limit])

The algorithm consists of repeating the following over and over:

- take the next available unmarked number in your list (it is prime)
- mark all the multiples of that number (they are not prime)

Repeat until you have processed each number in your range.

When the algorithm terminates, all the numbers in the list that have not been marked are prime.

The wikipedia article has a useful graphic that explains the algorithm: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Notice that this is a very specific algorithm, and the tests don't check that you've implemented the algorithm, only that you've come up with the correct list of primes.

There are two different methods of getting set up to run the tests with Objective-C:

- Create an Xcode project with a test target which will run the tests.
- Use the ruby gem
`objc`

as a test runner utility.

Both are described in more detail here: http://exercism.io/languages/objective-c

When submitting an exercise, make sure your solution file is in the same directory as the test code.

The submit command will look something like:

```
exercism submit <path-to-exercism-workspace>/objective-c/sieve/Sieve.m
```

You can find the Exercism workspace by running `exercism debug`

and looking for the line beginning
with Workspace.

Sieve of Eratosthenes at Wikipedia http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

```
#import <XCTest/XCTest.h>
#if __has_include("SieveExample.h")
# import "SieveExample.h"
# else
# import "Sieve.h"
#endif
@interface SieveTest : XCTestCase
@end
@implementation SieveTest
- (void)testAFewPrimes {
NSArray<NSNumber *> *expected = @[@2, @3, @5, @7];
XCTAssertEqualObjects(expected, [Sieve primesUpTo:10]);
}
- (void)testPrimes {
NSArray<NSNumber *> *expected = @[@2, @3, @5, @7, @11, @13, @17, @19, @23, @29, @31, @37, @41, @43, @47, @53, @59,
@61, @67, @71, @73, @79, @83, @89, @97, @101, @103, @107, @109, @113, @127,
@131, @137, @139, @149, @151, @157, @163, @167, @173, @179, @181, @191,
@193, @197, @199, @211, @223, @227, @229, @233, @239, @241, @251, @257,
@263, @269, @271, @277, @281, @283, @293, @307, @311, @313, @317, @331,
@337, @347, @349, @353, @359, @367, @373, @379, @383, @389, @397, @401,
@409, @419, @421, @431, @433, @439, @443, @449, @457, @461, @463, @467,
@479, @487, @491, @499, @503, @509, @521, @523, @541, @547, @557, @563,
@569, @571, @577, @587, @593, @599, @601, @607, @613, @617, @619, @631,
@641, @643, @647, @653, @659, @661, @673, @677, @683, @691, @701, @709,
@719, @727, @733, @739, @743, @751, @757, @761, @769, @773, @787, @797,
@809, @811, @821, @823, @827, @829, @839, @853, @857, @859, @863, @877,
@881, @883, @887, @907, @911, @919, @929, @937, @941, @947, @953, @967,
@971, @977, @983, @991, @997];
XCTAssertEqualObjects(expected, [Sieve primesUpTo:1000]);
}
@end
```

```
#import <Foundation/Foundation.h>
@interface Sieve : NSObject
+ (NSArray *)primesUpTo:(NSInteger)limit;
@end
```

```
#import "Sieve.h"
@implementation Sieve
+ (NSArray *)primesUpTo:(NSInteger)limit {
NSMutableArray *result = [NSMutableArray array];
for (NSInteger i = 2; i <= limit; ++i) {
[result addObject:@(i)];
}
NSInteger prime = 2;
NSInteger index = 0;
while ([[result lastObject] integerValue] >= prime * prime) {
for (NSInteger i = prime; i <= [result.lastObject integerValue] / prime; ++i) {
[result removeObject:@(i * prime)];
}
index++;
prime = [result[index] integerValue];
}
return result;
}
@end
```

A huge amount can be learned from reading other peopleâ€™s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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